Question: What's the first wrong statement in the proof below that $ \triangle BCE \cong \triangle BCA$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. $A$ $B$ $C$ $D$ $E$ $F$ Givens $ \overline{BC} \cong \overline{BD}$ $, \ $ $ \angle ABC \cong \angle DBE$ $, \ $ $ \angle BAC \cong \angle BED$ $, \ $ $ \angle ACB \cong \angle ECF$ $, \ $ $ \overline{BC} \cong \overline{CF}$ $, \ $ and $\ $ $ \angle ABC \cong \angle CFE$ Proof $ \triangle BDE \cong \triangle BCA$ because AAS $ \overline{BE} \cong \overline{AB}$ because corresponding parts of congruent triangles are congruent $ \angle BCE \cong \angle CEF$ because alternate interior angles are equal $ \angle BED \cong \angle CBE$ because alternate interior angles are equal $ \angle BCE \cong \angle CEF$ because alternate interior angles are equal $ \triangle BCE \cong \triangle BCA$ because SSS
Solution: Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. $ \overline{CE} \cong \overline{BE}$ is the first wrong statement.